A GaN-based semiconductor is a compound semiconductor represented by the general formula AlaInbGa1-a-bN (0≦a1, 0≦b≦1, 0≦a+b≦1), which is also called a III group nitride semiconductor, a nitride-based semiconductor or the like. GaN-based semiconductor light emitting elements such as an LED (light emitting diode) and an LD (laser diode), in which a pn-junction type light emitting element structure comprising the GaN-based semiconductor is formed on a substrate, have come into practical use, and are becoming widely used as light sources for display devices and illuminating devices.
Of the GaN-based semiconductor light emitting elements, in the manufacture of the LD, a GaN single crystal substrate is mainly used. On the other hand, in the manufacture of the LED, a sapphire single crystal substrate is mainly used. GaN-based semiconductor crystals having various kinds of orientations can be allowed to epitaxially grow on a single crystal substrate made of GaN or sapphire. However, used in the GaN-based semiconductor light emitting elements which have come into practical use at present is a c-axis-oriented GaN-based semiconductor crystal. Although the sapphire single crystal substrate includes a c-plane substrate, an a-plane substrate, an r-plane substrate and the like, the c-plane substrate is suitable for the manufacture of the c-axis-oriented GaN-based semiconductor crystal. Incidentally, nowadays, it has become a common view among those skilled in the art that the substrate called the c-plane substrate includes a substrate having a surface slightly inclined from the c-plane (a so-called off-angled substrate) (the same also for the a-plane substrate, the r-plane substrate and the like).
The GaN-based semiconductor crystal which epitaxially grows on the c-plane sapphire substrate becomes one comprising dislocation defects at high density which are caused by lattice mismatch. As one of methods for solving this problem, there has been developed an epitaxial growth technique which generates a lateral growth mode of a GaN-based semiconductor crystal by processing a substrate surface to an uneven surface by a method such as etching (LEPS: Lateral Epitaxy on a Patterned Substrate) (patent document 1 and patent document 2). Further, it has been known that when a GaN-based semiconductor light emitting element is formed using a sapphire substrate in which the surface for semiconductor crystal growth is processed to an uneven surface (hereinafter also referred to as a “patterned sapphire substrate”), an effect of increasing the light extraction efficiency is obtained, aside from the effect of reducing the dislocation defects (patent document 3).    Patent Document 1: WO 2000/55893 pamphlet    Patent Document 2: WO 2002/23604 pamphlet    Patent Document 3: WO 2002/75821 pamphlet